Motion in a Straight Line

The juggler throws n balls per second.
∴ Interval between balls =‌

1

n

seconds At maximum height velocity of first ball v=0
Juggler throws all balls with same initial velocity =u
For 1 st ball,
u1=u,v1=0,a=−g,S=Hmax
Using formula,
v2=u2+2as
0=u2−2gHmax
⇒Hmax=‌

u2

2g

......‌ (1) ‌
And using formula,
v=u+at
⇒0=u−gt
⇒t=‌

u

g

∴ Time taken by ball 1 to reach maximum height (Hmax)=‌

u

g

According to the question,
t=‌

1

n

⇒‌

u

g

=‌

1

n

⇒u=‌

g

n

......(2)
Putting value of u in equation (1), we get
Hmax=‌

( g n )2

2g

=‌

g2

2n2g

=‌

g

2n2